Ajinkya Rahane sent a 146kph bouncer from Pat Cummins flying into the crowd at midwicket and, next ball, slapped another short one over the cover fence while backing away. These were the blows that finally snuffed out the last of Australia's fight, and sealed once and for all India's victory in this most bewitching of Border-Gavaskar series.

Australia entered the fourth morning with only the scantest of hopes, defending a mere 87 runs and needing 10 wickets. This did not mean that contest was over, as Josh Hazlewood and Pat Cummins fired the ball down with pace and venom after a night's refreshment. The loss of M Vijay and Cheteshwar Pujara - the latter run out by a brilliant throw from Glenn Maxwell - kept Australia hoping. But KL Rahul and Rahane responded with bold blows to settle the matter.

The win in Dharamsala ended India's marathon home Test season with four series victories out of four, and also means that the team presently holds series honours over every other nation in the five-day game. Rahane's stand-in captaincy, in the absence of the injured Virat Kohli, had been vital to this achievement, so too the runs of Rahul, the pace of Umesh Yadav and the all-round contribution of Ravindra Jadeja. There will be great satisfaction derived also from the fact that Dharamsala offered conditions more familiar to the tourists.

For that reason, among others, Steven Smith's team were left to ponder a string of missed opportunities after their vast opening win in Pune. There have been times in all three Tests since that the Australians have looked very much in control of proceedings, but they have been unable to stay on the mountaintop under pressure from an Indian side roused into action by the shock of that first-up hiding.

As the ball continued to bounce and swerve when India resumed their pursuit of a modest target today, Australia's fielders must have wondered what might have been with another 100 or so runs to defend. Josh Hazlewood went up for a pair of vociferous lbw appeals against Vijay in the opening over, but on both occasions the opener got the merest of bat to ball before it struck the pad.

At the other end Cummins sent a bouncer down the leg side that may have touched Vijay's gloves before being taken on the juggle by Matthew Wade. Certainly Ultra Edge indicated as much, but only Wade raised the most half-hearted of appeals. More straightforward was another edge in Cummins' next over, near enough to an action replay of Vijay's first-innings dismissal, which offered a glimmer of light for Australia.

Genuine excitement followed when Pujara and Rahul hesitated fatally in taking a quick single to the right arm of Maxwell, who threw down middle stump to send Pujara on his way with 60 still needed. In those moments the Australians wondered briefly what might be possible, and the Indian viewing area tensed up like with so many teams chasing a pesky small target in the past.

But Rahane and Rahul barely put a foot out of place in the overs that followed, accumulating steadily until Cummins elected to go around the wicket for the tourists' final effort. Rahane's riposte, the first impressively orthodox, the second more redolent of the forthcoming IPL, said much about India's admirable resilience in the face of a most unexpected challenge.